Smeeth said she knew Corbyn would condemn the messages but that he needed to do more than that because many were sent by people who claimed to support him.

“It’s vile, it’s disgusting and it’s done in the name of the leader of the Labour party, which makes it even worse,” Smeeth told BBC2’s Victoria Derbyshire programme.

“I know that Jeremy Corbyn would condemn this, but it’s not about condemning, it’s about what people are doing in his name.

“What I need is for the leader of my party, the leader of Her Majesty’s opposition, to make it clear what can be done. He should be naming and shaming some of the worst perpetrators who are doing it in his name, and making it clear publicly that they do not speak for him, that this is unacceptable.

“There is a vile amount of racism and intolerance and abuse online, which then feeds on to our streets and leads to a culture of intolerance that he could actually personally do something about. That’s what I’m asking him to do.”

Politics is not a game. Words of hate have consequences | Gaby Hinsliff

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She said 20,000 pieces of abuse arrived within 12 hours of the launch event but another 5,000 came in the subsequent weeks.

“Most of it was on social media, most of it on Twitter, a great deal on Facebook, and then calls to my office and emails,” she said.

One message which had been passed to the police branded the MP a “dyke” and a “CIA agent”. The message accused her of treason and said the gallows would be a “fine and fitting place” for her.

A spokesman for Corbyn said: “Jeremy has consistently spoken out against all forms of antisemitism and has contacted Ruth Smeeth to express his outrage at the abuse and threats directed against her.

“Jeremy condemns all abuse, and no one responsible for it is a genuine supporter of Jeremy’s. He has repeatedly called for a kinder, gentler politics.

“This is why he launched Respect and Unity, a code of conduct calling on all Labour members and supporters to conduct themselves with a high standard of behaviour. Evidence of threats and abuse should be reported to the party and police so that action may be taken against those responsible.”

The messages began in June when Smeeth walked out of the Corbyn and Chakrabarti press conference after being accused of colluding with the Daily Telegraph in a row over leaflets criticising MPs opposed to the leadership.

In a statement at the time, Smeeth said: “I was verbally attacked by a Momentum activist and Jeremy Corbyn supporter who used traditional antisemitic slurs to attack me for being part of a ‘media conspiracy’.

“It is beyond belief that someone could come to the launch of a report on antisemitism in the Labour party and espouse such vile conspiracy theories about Jewish people, which were ironically highlighted as such in Ms Chakrabarti’s report, while the leader of my own party stood by and did absolutely nothing.”

The Metropolitan police confirmed their counterterrorism command was conducting an investigation into allegations of malicious communication and threats to kill made via social media.

Chris Bryant, the former shadow leader of the House of Commons, said this week that threats against MPs appeared to be rising, with those who were gay, female or from an ethnic minority receiving the worst treatment.

People have been prosecuted in recent months for making death threats to the Labour MPs Luciana Berger and Ben Bradshaw, while fellow party MP Jess Phillips is having a “panic room” fitted in her constituency office after a series of threats to her safety. A number of others are having security enhancements made to their homes and constituency offices amid heightened fears of attacks.